Question

In cyclic quadrilateral PQRS ,5✓Q=7✓S then find ✓Q

Answer 1

The value is $\sqrt{Q} =105$

Explanation:

It is given that PQRS is a cyclic quadrilateral.

Also, given that $5\sqrt{Q} =7\sqrt{S}$

Now, we shall determine the value of $\sqrt{Q}$

Since, we know that in a cyclic quadrilateral, the sum of opposite angles add upto 180°

Thus, we shall add the two angles Q and S.

Hence, we have,

$\sqrt{Q}+\sqrt{S}=180$

Substituting the value of $\sqrt{S}$ from the expression $5\sqrt{Q} =7\sqrt{S}$, we have, $\frac{5\sqrt{Q}}{7} =\sqrt{S}$

Hence, we get,

$\sqrt{Q}+\frac{5 \sqrt{Q}}{7}=180$

Simplifying, we have,

     $\frac{7\sqrt{Q} +5\sqrt{Q} }{7} =180$

$7 \sqrt{Q}+5 \sqrt{Q}=1260$

          $12 \sqrt{Q}=1260$

              $\sqrt{Q}=105$

Thus, the value is $\sqrt{Q}=105$

Learn more:

(1) Find the four angles of a cyclic quadrilateral ABCD in which angle A=(2x-1) , angle B=(y+5) , angle C=(2y+15) and angle D=(4x-7).

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(2) In a cyclic quadrilateral abcd , twice the measure of angle a is thrice the measure of angle c find the measure of angle c

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